Noncommutative geometry and fundamental interactions

T. Krajewski

RECORD

Noncommutative geometry and fundamental interactions

T. Krajewski

Mathematical Physics · Submitted 30 Mar 1999

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory.

how it is stated · asserted 0.92 read the record →

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,012 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral triples, differential calculus or gauge theories on projective modules. Within this framework, The index theorem and cyclic homology are applied to the probe of topologically non trivial properties of Chern-Simons and Yang-Mills action functionals in dimension 3 and 4. Following earlier work on the standard model in noncommutative geometry, it also provides a general study of all Yang-Mills-Higgs models based on space-times structures which are the product of usual space-time by a discrete space, with emphasis on the physical properties of the resulting theories. Finally, the last part is devoted to the development of classical and quantum gauge theory on the noncommutative torus in any dimension. It includes a discussion of topological properties and symmetries of the action as well as its perturbative quantization.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory.	contribution 0.86	0.44	0.06	asserted 0.92
s1	It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral triples, differential calculus or gauge theories on projective modules.	background 0.79	0.43	0.02	asserted 0.99
s2	Within this framework, The index theorem and cyclic homology are applied to the probe of topologically non trivial properties of Chern-Simons and Yang-Mills action functionals in dimension 3 and 4.	contribution 0.82	0.76	0.08	asserted 1.00
s3	Following earlier work on the standard model in noncommutative geometry, it also provides a general study of all Yang-Mills-Higgs models based on space-times structures which are the product of usual space-time by a discrete space, with emphasis on the physical properties of the resulting theories.	contribution 1.00	0.84	0.10	asserted 0.99
s4	Finally, the last part is devoted to the development of classical and quantum gauge theory on the noncommutative torus in any dimension.	contribution 1.00	0.83	0.05	asserted 0.96
s5	It includes a discussion of topological properties and symmetries of the action as well as its perturbative quantization.	contribution 0.95	0.72	0.05	asserted 0.92

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 0.92.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral triples, differential calculus or gauge theories on projective modules. Within this framework, The index theorem and cyclic homology are applied to the probe of topologically non trivial properties of Chern-Simons and Yang-Mills action functionals in dimension 3 and 4. Following earlier work on the standard model in noncommutative geometry, it also provides a general study of all Yang-Mills-Higgs models based on space-times structures which are the product of usual space-time by a discrete space, with emphasis on the physical properties of the resulting theories. Finally, the last part is devoted to the development of classical and quantum gauge theory on the noncommutative torus in any dimension. It includes a discussion of topological properties and symmetries of the action as well as its perturbative quantization.

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